Fast Formation Control of Second-order Multi-agent Systems with Time-varying Reference Velocity

To solve the fast formation control problem of second-order multi-agent systems, an analytical design approach for the optimal distributed control protocol is proposed to track the time-varying reference velocity while achieving the fastest formation. Firstly, the formation control problem of the original system is transformed to the consensus problem of the deviation system by model transformation, and necessary and sufficient conditions to achieve the formation are given. Secondly, explicit expressions of the optimal convergence rate and corresponding control gains to achieve the fastest formation are obtained by the Jury criterion. Finally, the validity of theoretical results is verified by simulation experiments.